It's not really clear, even the admin isn't too sure how it all works but here is my best guess.
You recieve + or - Rep when another member credits your post. The degree of how much you gain or lose is controlled by the issuers Rep Power. (For example if a n00b or alias account +reps your post it will probably rise by 1 point but if an admin credits your post then likely it will rise by alot more.)
Your Rep points (viewable via the User CP) contributes to how many 'gems' you have to your name.
These increase after a certain rep point milestone (quantity). Rep points also add to your own Rep Power but, this is also calculated by other factors such as length of membership and frequency of activity (posts per day) and others.
In general someone who posts decent quality posts regularly will quickly become popular and 'reputable' among the forums.
If you want to aquire rep as a bragging right to authority then just be nice and don't post some BS comments. From what I've seen, posting links in the PSN Store Links thread seems to be a good way to earn +Rep as Aldostools is doing quite fine in his Rep in such a short time.
Hope this clears things up for alot of people out there. Happy posting!
Go earn those Rep Points!!